Representations of non-negative polynomials having finitely many zeros

DOI10.5802/afst.1131zbMath1130.13015OpenAlexW2325451489MaRDI QIDQ2372654

Murray A. Marshall

Publication date: 1 August 2007

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_2006_6_15_3_599_0

zbMATH Keywords

semi-algebraic setreal algebraic varietyquadratic moduleArchimedeanring of continuous functionscoordinate ringpositive function

Mathematics Subject Classification ID

Semialgebraic sets and related spaces (14P10) Real algebra (13J30)

Related Items (7)

Finite Convergence of Sum-of-Squares Hierarchies for the Stability Number of a Graph ⋮ On the complexity of Putinar's Positivstellensatz ⋮ Optimality conditions and finite convergence of Lasserre's hierarchy ⋮ Second Order Conditions to Decompose Smooth Functions as Sums of Squares ⋮ Semidefinite relaxations for semi-infinite polynomial programming ⋮ A survey on conic relaxations of optimal power flow problem ⋮ Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities

Cites Work

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• The \(K\)-moment problem for compact semi-algebraic sets
• Sums of squares on real algebraic curves
• Distinguished representations of non-negative polynomials
• Distinguished representations of strictly positive polynomials
• Optimization of Polynomial Functions
• Sums of squares of regular functions on real algebraic varieties
• Optimisation globale et théorie des moments
• Positivity, sums of squares and the multi-dimensional moment problem II
• A representation theorem for certain partially ordered commutative rings

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